Question

Area of rhombus is 96 sq.cm.
one of the diagonals is 12 cm
find the length of its side.
( explain in details)​​​

Answer 1

Given :-  

• Area of rhombus is 96 sq.cm.

• One of the diagonals is 12 cm

To Find :-  

• Find the length of its side.

Solution :-  

~Here, we’re given the area of the rhombus and one of it’s diagonals . We need to find the side of the rhombus. Firstly, we’ll find the length of other diagonal by putting the values in the formula of it’s area. Then, we can find the side by applying the Pythagoras theorem.  

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As we know that ,  

$\boxed{\sf{ \maltese \;\; Area\;of\;rhombus = \dfrac{1}{2} \times a \times b }}$

Where,  

• a and b are the diagonals  

$\boxed{\sf{ \maltese \;\; Pythagoras\;theorem \rightarrow A^{2} + B^{2} = C^{2} }}$

Where,  

• A , B are adjacent sides and C is the hypotenuse  

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Finding the other diagonal :-  

$\sf \implies 96 = \dfrac{1}{2} \times 12 \times b$

$\sf \implies b = \dfrac{96 \times 2}{12}$

$\boxed{\bf{ \bigstar \;\; Other\;diagonal = 16\;cm}}$  

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→ Let the side be x cm  

→ AO = 16 ÷ 2 = 8 cm  

→ OB = 12 ÷ 2 = 6 cm  

[ Diagonals of rhombus perpendicularly bisect each other, so the formation of the rhombus will be as given in diagram ]  

Finding the side :-  

$\sf \implies AO^{2} + OB^{2} = x^{2}$

$\sf \implies 8^{2} + 6^{2} = x^{2}$

 $\sf \implies 64 + 36 = x^{2}$

$\sf \implies 100 = x^{2}$ 

$\sf \implies \sqrt{100} = x$

$\boxed{\bf{ \bigstar \;\; Side = 10\;cm}}$

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Hence,  

• The side of the rhombus is 10 cm  

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